Mastering the Statistical Report: A Cambridge Year 12 Statistics Writing Framework and Model | 掌握统计报告：剑桥12年级统计写作框架与范文

📚 Mastering the Statistical Report: A Cambridge Year 12 Statistics Writing Framework and Model | 掌握统计报告：剑桥12年级统计写作框架与范文

Writing a statistical investigation report is a crucial skill in the Cambridge Year 12 Statistics curriculum. This article provides a structured writing framework and a complete model example to guide you through every section, from defining a research question to drawing evidence-based conclusions. By following this framework, you will learn to present data clearly, conduct appropriate analyses, and interpret results in context. The model example investigates the relationship between daily social media use and sleep duration among Year 12 students.

撰写统计调查报告是剑桥12年级统计学课程中的关键技能。本文提供一个结构化的写作框架和一份完整的范文，指引你完成从提出研究问题到得出基于证据的结论的每一步。通过遵循该框架，你将学会清晰地呈现数据、进行恰当的分析并结合背景解读结果。范文示例探究了12年级学生每日社交媒体使用时间与睡眠时长的关系。

1. Understanding the Purpose of a Statistical Report | 理解统计报告的写作目的

A statistical report communicates the entire statistical enquiry cycle: posing a meaningful question, planning and collecting data, organising and analysing it, and finally presenting findings with a critical eye. In Cambridge assessments and coursework tasks, you are expected to demonstrate statistical literacy, correct use of graphs, accurate calculations, and thoughtful interpretation. The report should read like a coherent story, not a disjointed list of outputs.

统计报告传达完整的统计探究周期：提出有意义的问题，规划并收集数据，整理和分析数据，最后以批判性的眼光呈现发现。在剑桥评估和课程作业中，要求你展示统计素养、正确使用图表、准确计算以及深思熟虑的解读。报告应该像连贯的故事，而非零散的输出列表。

2. Defining the Research Question | 确定研究问题

Begin with a clear, focused research question. For our model report, we ask: ‘Is there a negative linear correlation between daily social media use (hours) and nightly sleep duration (hours) among Year 12 students?’ After stating the question, formulate the null and alternative hypotheses. Here, H₀: ρ = 0 (no linear correlation in the population) and H₁: ρ < 0 (negative correlation). A one‑tailed alternative is chosen because existing research suggests a negative direction.

首先提出清晰且聚焦的研究问题。在范文报告中，我们的问题是：“12年级学生每日社交媒体使用时长（小时）与夜间睡眠时长（小时）之间是否存在负线性相关？”陈述问题后，设立原假设和备择假设。本例中，H₀: ρ = 0（总体中无线性相关），H₁: ρ < 0（负相关）。选择单尾备择假设是因为现有研究提示方向为负。

3. Planning Data Collection | 规划数据收集

Describe your sampling strategy and data collection instruments. Our model study used a simple random sample of 30 Year 12 students from a large secondary school. Each participant completed a diary, recording daily social media hours and sleep hours over a typical school week. Averages were computed to reduce day‑to‑day fluctuation. Ethical protocols were followed: informed consent was obtained, and all responses remained anonymous. A pilot survey with five students helped refine the wording of the diary sheet.

描述你的抽样策略和数据收集工具。范文研究从一所大型中学的12年级学生中简单随机抽取了30人。每名参与者完成一份日记，记录一个典型上学周内每日的社交媒体小时数和睡眠小时数。计算均值以减少每日波动。严格遵循伦理规范：获得知情同意，所有回答均保持匿名。对五名学生进行的试点调查帮助改进了记录表的措辞。

4. Describing the Sample and Variables | 描述样本与变量

The sample comprises 30 students aged 16–17. The explanatory variable is ‘social media use’ (continuous, measured in hours per day), and the response variable is ‘sleep duration’ (continuous, measured in hours per night). Both are numerical, bivariate data. We note that the sample size, while modest, meets the minimum requirement for a correlation analysis if assumptions are checked later. A table of descriptive statistics will summarise the variables.

样本由30名16–17岁的学生组成。解释变量是“社交媒体使用时长”（连续型，以小时/天衡量），响应变量是“睡眠时长”（连续型，以小时/晚衡量）。两者均为数值型双变量数据。我们注意到，样本量虽然不大，但只要后续检查假设，就能满足相关分析的最低要求。后续将用描述性统计表概括变量。

5. Data Presentation: Tables and Graphs | 数据呈现：表格与图表

Present a portion of the raw data in a neatly labelled table, then display the full dataset graphically. For our model, we show the first eight observations. A scatterplot with social media hours on the x‑axis and sleep hours on the y‑axis follows. The plot reveals a pronounced downward trend, with most points falling from top‑left to bottom‑right.

在标注整洁的表格中呈现部分原始数据，然后用图形展示完整数据集。在范文中，我们展示前八个观测值。随后绘制散点图，x轴为社交媒体小时数，y轴为睡眠小时数。图形显示明显的下降趋势，多数点从左上方落向右下方。

The scatterplot (not shown here due to format, but you would include an accurate, fully labelled graph) confirms a potential negative correlation. Outliers are not obvious, and the pattern appears roughly linear. This visual inspection justifies proceeding with Pearson’s correlation and linear regression.

散点图（由于格式限制此处未展示，但你在实际报告中应包含准确、标注完整的图形）证实了潜在的负相关。离群值不明显，模式大致呈线性。这一目视检查表明可以继续使用皮尔逊相关系数和线性回归。

6. Descriptive Statistics: Measures of Centre and Spread | 描述性统计：中心与离散度量

Calculate means and sample standard deviations for both variables. Using the full dataset of 30 students, we obtained:
Social media use: mean x̄ = 5.1 h, standard deviation sₓ = 1.5 h.
Sleep duration: mean ȳ = 7.1 h, standard deviation s_y = 0.82 h.
The standard deviations indicate spread: social media use varies more across students than sleep does. A summary table of these statistics, along with the five‑number summary, gives the reader an immediate sense of central tendency and dispersion. The mean social media use exceeds five hours, which suggests a relatively high usage among the sampled adolescents.

计算两个变量的均值和样本标准差。使用全部30名学生数据，我们得到：
社交媒体使用：均值 x̄ = 5.1 小时，标准差 sₓ = 1.5 小时。
睡眠时长：均值 ȳ = 7.1 小时，标准差 s_y = 0.82 小时。
标准差显示了离散程度：社交媒体使用在不同学生间的变异大于睡眠。将这些统计量与五数摘要一起列入汇总表，能让读者对集中趋势和离散程度一目了然。平均社交媒体使用超过五小时，表明被抽样青少年使用时间较高。

7. Exploring Relationships: Correlation and Regression | 探索关系：相关与回归

Pearson’s correlation coefficient r quantifies the strength and direction of the linear relationship. From the data, r = −0.78. This is a strong negative correlation: as social media use increases, sleep tends to decrease. Next, we fit the least squares regression line ŷ = a + bx. The slope is b = r × (s_y / sₓ) = −0.78 × (0.82/1.5) ≈ −0.426. The intercept is a = ȳ − b x̄ = 7.1 − (−0.426)×5.1 ≈ 9.27. Therefore, the regression equation is:

皮尔逊相关系数 r 用来量化线性关系的强度和方向。根据数据，r = −0.78。这是一个强负相关：社交媒体使用增加时，睡眠时长趋于减少。接着，我们拟合最小二乘回归直线 ŷ = a + bx。斜率 b = r × (s_y / sₓ) = −0.78 × (0.82/1.5) ≈ −0.426。截距 a =

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